If you are using Bootstrap 4, its grid uses Flexbox, so the columns in the row should already match each other's height. You can then use Bootstrap 4's Flexbox utility classes to vertically center the column's content: class="d-flex align-items-center". Ex:

If you are using Bootstrap 3, you're going to have to add the appropriate flexbox code to both get your columns to match in height and vertically center your content. Here is a little cheatsheet I find helpful for building out flexbox layouts: http://jonibologna.com/flexbox-cheatsheet/